MEE 210 Exam 1

Unit vector Ua

(Ax/A)i + (Ay/A)j + (Az/A)k where A = sqrt(Ax^2 + Ay^2 + Az^2)

A x B (cartesian)

(AyBz - AzBy)i - (AxBz - AzBx)j + (AxBy - AyBx)k

slug units

(lb x s^2) / ft

-> F (vector) =

-> |F| x u

A x B

-B x A

k x j

-i

i x k

-j

j x i

-k

i x i j x j k x k

0

1 ft

0.3048 m

milli

10^-3 w/ prefix of m

micro

10^-6 w/ prefix of u

nano

10^-9 w/ prefix of n

kilo

10^3 w/ prefix of k

mega

10^6 w/ prefix of M

giga

10^9 w/ prefix of G

1 slug (mass)

14.59 kg

1 lb (force(

4.448 N

G (constant of gravitation)

66.73 x 10^-12 m^3/(kgs^2)

sum of the forces that are acting on an object

= 0

cartesian vector representation

A = Axi + Ayj + Azk

Magnitude of a cartesian vector

A = sqrt(Ax^2 + Ay^2 + Az^2)

Vector

A quantity that has magnitude and direction

Magnitude of C (cross product)

ABsin(theta)

magnitude of the projection of a vector

Aa = A (dot) Ua

Force (spring)

F = ks

Force between two objects

F=G(m1m2/r^2)

Force

F=ma

X component of a force

Fcos(theta)

Moment Mo

Fd

Resultant Force

Fr = F1 + F2

Y component of a force

Fsin(theta)

vector addition

R = A + B

Vector subtraction

R = A - B = A + (-B)

parallelogram law

System of determining the resultant force of 2 concurrent forces obtained from the diagonal at a parallelogram having adjacent sides which represent the 2 force vectors being added

Unit vector from A to B

Uab = [(Xa - Xb)i + (Ya - Yb)j + (Za-Zb)k]

-> F (components) =

^ ^ Fxi + Fyj

rigid body

a combination of a large number of particles in which all the particles remain at a fixed distance from one another, both before and after applying a load

When solving for F or theta, use

a free body diagram and split into components

scalar

a physical quantity that has magnitude but no direction

multiplication/division of a vector by a scalar will

change the magnitude of the vector

On a pulley, tension in the ropes are

equal

US customary units

foot, second, slug, pound

Triangle Law

head to tail vector addition

j x k

i

r (cross) F

i j k rx ry rz Fx Fy Fz

k x i

j

i x j

k

four basic quantities

length, time, mass, force

SI units

meter, second, kilogram, newton

Mo

r (cross) F

position vector

r = xi + yj + zk

k

stiffness of the spring

s

stretch length of the spring

Unit vector

v/(|v|)

A (dot) B

|A||B|cos(theta), where theta is between 0 and 180 or AxBx + AyBy + AzBz